In Section 1.6 we presented the track outputs of the industrial object tracking application and the developed PGM, and briefly discussed the results. We noted that whereas the majority of tracks were plausible and consistent between the two models, there were also cases where there were discrepancies and seemingly incorrect results. In this section we will discuss some of these cases. Figure 10.9 below shows the real radar detections overlaid on a satellite image. The outputs of the developed model and the industrial model are given again here (see Figures 10.7 and 10.8 below) for convenience.
Figure 10.7: Industrial model track estimates (units in meters). Note the relatively dense clutter. Detections (black o’s), tracks (colour lines)
Figure 10.8: PGM model track estimates (units in meters). Note the relatively dense clutter. Detections (black o’s), tracks (colour lines)
Figure 10.9: Real radar detection data and PGM track estimates overlaid on a satellite image. The data was recorded in the Kruger National Park. The radar detections are indicated by black circles and the different colours indicate different tracks. The ‘a’ and ‘c’ circles indicate areas where there are discrepancies between the output of the PGM and the industrial multiple target tracking application. The detections at ‘b’ seem to form a track, although no track is present here in either the industrial model or the PGM outputs.
The green track at ‘a’ shows one of the tracks that are not present in the industrial model track estimates. This is believed to be a motor vehicle, since the track aligns almost perfectly with a (dirt) road. The industrial application was set up to track relatively slow moving objects and this track has an average velocity of about 60 km/h. This could be the reason that it is not present in the industrial application’s output. The detections that seem to form a track but have no associated track at ‘b’ are also aligned with a road, although this is a two-lane, paved road that should have more bi-directional traffic than the dirt road aligned with the track at ‘a’. The absence of tracks here could therefore be due to seemingly inconsistent dynamics due to bidirectional traffic and the relatively high speed of the traffic with respect to the effective detection frequency. It should be noted that the output of the industrial model also does not
contain tracks in this area. The large number of detections without tracks at ‘c’ are thought to be due to trees moving in the wind, as there are many trees in this area. Lastly , there are a few additional, short tracks that are present only in the PGM’s output. These tracks are believed to be clutter tracks, where a few false detections13 that were, by chance, generated in such a way that they seemed to form tracks and were then stopped by the clutter classification model when they generated no further detections. Some of these tracks could also have been added near the end of the filter operation and could therefore not have been removed by the clutter classification procedure. An example of these tracks can be seen in the area below ‘c’.
The plausibility of the above explanations notwithstanding, they are speculative and there is no hard evidence that they are indeed correct. Aside from these few explainable discrepancies, however, most of the tracks are consistent between the outputs of the two models. The track estimate plots of the two respective models can be seen in Section 1.6.
In the previous section, we have shown through simulations that the developed PGM can consistently and accurately track multiple targets in the presence of clutter and missed detec- tions. In this section we have presented an additional example that shows that the PGM is indeed capable of tracking real objects from real radar data.
10.5
Conclusion
In this chapter we discussed the similarities between the developed PGM and the traditional methods. Here we noted that, while the PGM is similar to the traditional methods in some low- level aspects, it is different from the traditional methods at a high level. Furthermore, it was shown that the PGM does not suffer from poor performance as the PHD filter does when there are multiple missed detections. Additional performance tests show that the PGM consistently offers high performance under many different and challenging circumstances. From these tests we have also seen that the computational complexity of the model is low in simple problems and automatically increases in order to maintain good performance when required. Lastly, the results of the real radar data test indicate that the PGM does not only work with simulated data, but can be applied to real-world problems.
This chapter concludes the discussion about the developed PGM. In the next and final chapter we will look back on the work that has been done and consider possible future work that can be done in order to further expand and improve the developed model.
Chapter 11
Conclusion And Future Work
11.1
Conclusion
The objective of this work was to develop a probabilistic graphical model for effective multiple object tracking. To this end, we have studied and discussed the necessary probability and PGM theory and shown how the theory can be applied to solve the multiple object tracking problem. Most of the theory that we have discussed in this work is, however, applicable to PGMs in general and is not limited to multiple object tracking applications. Similarly, the factor classes that were implemented in software are also very general and can be used to construct and perform inference in general, hybrid graphical models. These classes therefore also contribute important functionality to the EMDW library and could allow for faster development of future PGM applications.
Multiple object tracking is a complex problem and finding a solution to this problem is challenging. The approach taken to solve this problem was to start with an oversimplified graphical model and to incrementally increase functionality and complexity. To this end, we used the basic Kalman filter as the foundation for the developed model. We first investigated the connections between the Kalman filter algorithm and the corresponding graphical model. We then extended this model to allow multiple objects to be tracked by solving the data-association problem with the use of discrete association variables. Here we noticed that interesting and logical data-association characteristics arise automatically from the graph structure. This model could, however, only track a fixed and known number of targets and we therefore needed to extend its functionality further. Bayesian model selection was used to allow the model to automatically determine the number of targets. The model that was developed up to this point still had no mechanism for identifying false detections, and we concluded that this would be impossible on a single detection basis. We therefore used inspiration from the logical reasoning that a person might apply to solve the clutter problem and implemented similar probabilistic logic in a PGM. This model was integrated into the object-tracking PGM, allowing the model to
infer the probability that a track is real by considering all the possible detections in the context of the larger track instead of focussing on single detections. The improved model finally had all the necessary functionality for tracking multiple targets in a realistic setting.
The model developed thus far was, however, found to be very computationally expensive and would therefore be practically unusable for tracking a large number of targets. In order to increase efficiency, we first focussed on the most computationally expensive aspect of the model - the model selection subroutine. Here we discovered that model selection can be performed much more efficiently through inference in a single graph. This was a surprisingly elegant solution, as it allowed both variable inference and structure learning to be performed through message passing. With the more efficient model selection method successfully implemented, we turned our attention to a seemingly unnecessary and computationally expensive characteristic of the developed model. This was the fact that the model considered the possibility that any detection could be associated with any target on the map no matter how far away the detection was from the target. In order to improve efficiency on this aspect of the model, a detection gating subroutine was implemented in order to efficiently rule out unlikely detection associations and allow for more sparsely connected graphs to be constructed. These two improvements vastly increased the efficiency of the model.
Next we turned our attention to the tracking accuracy of the model. Here we focussed on one of the approximations that is made by the model - the moment matching approximation of Gaussian mixtures. The reason that we could not make proper use of Gaussian mixtures in the model was that Gaussian mixture quotients do not generally have a Gaussian mixture form. This conflicts with our closed-form requirement for operations on distributions, and no solution to this problem could be found in the literature. We therefore sought to find a method for approximating a Gaussian mixture quotient as a Gaussian mixture. We designed an algorithm to perform this approximation and tested the performance of the algorithm. It was found that the algorithm can determine almost the exact Gaussian mixture when the true quotient function is a Gaussian mixture, and that it often yields good approximations even when it is not. The extent to which the use of this algorithm would make a difference in an MOT application was still unclear, since there are good reasons why the moment matching approximation should be accurate in the majority of situations that will arise in such an application (discussed in Section 6.2). It was, however, shown that the proper use of Gaussian mixtures, which is enabled by the developed algorithm, can increase performance in certain challenging scenarios. It was also shown that the use of the algorithm can make the difference between correct and incorrect track identifications (see Section 8.3).
Finally, the completed model was compared to the existing, traditional multiple object track- ing algorithms. Here it was found that the PGM shares some low-level aspects with the tradi- tional models, but that it is more general at a high level. The developed PGM with the clutter track classification functionality also has the advantage that it does not require the clutter den- sity or detection probability to be known. Furthermore, it was shown that the PGM does not suffer from poor performance when there are frequent missed detections, as the PHD filter does.
In order to assess the performance of the developed PGM in a statistically meaningful man- ner, a large number of random tests where performed. Here it was found that the PGM can consistently and accurately track multiple targets in challenging scenarios and under a wide range of circumstances. Finally, the model was tested on real radar data through a qualita- tive comparison with an industrial model. The results of the outputs were largely similar and possible explanations for the few discrepancies were given. The results of this test indicate that the model not only works in a simulated environment, but can also be used in real-world applications.
In this work we have therefore shown that probabilistic graphical models can be successfully used for multiple object tracking, and that some improvements can be made to some of the existing algorithms.